In the absence of any information regarding the acquisition of share…

The correct answer is Option (1) → Old Profit Sharing Ratio

When nothing is said about how the remaining partners take up the outgoing partner’s share, they are taken to share it in their old profit sharing ratio; their new ratio then stays the same as their old ratio between themselves, and the gaining ratio equals the old ratio.

Option (2) New Profit Sharing Ratio — Incorrect. The new ratio is itself what is being worked out from this assumption.

Option (3) Equal Ratio — Incorrect. Equal sharing applies only where the partners agree to it.

Option (4) Capital Ratio — Incorrect. Capitals have no bearing on profit sharing unless the partners agree so.